“Call Me by Your Name,” a gay coming-of-age romance set at an Italian villa in the summertime (the best possible location for such a story), isn’t sexual so much as hormonal. It’s not about doin’ it; it’s about wanting to do it, about discovering what “it” even is. Drenched in sunlight, the movie is filled with warmth (and hotness), devoid of sappy melodrama but rich with honest emotion that transcends boundaries of sexual orientation. This romance may not have the physical features of the ones you’ve had, but you’ve probably felt this longing.

It is 1983. Oliver (Armie Hammer), a strapping twentysomething grad student who looks like Armie Hammer, arrives at the summer home of Prof. Perlman (Michael Stuhlbarg), his wife (Amira Casar), and their 17-year-old son, Elio (Timothée Chalamet). The Perlmans are multicultural polymaths, fluent in a few languages, well-monied and socially liberal, affectionate as a family. Elio, a willowy, introverted teen, is typically bored with the students who come to work with his father each summer, but he’s fascinated by Oliver’s casual confidence and simultaneously put off by his cockiness.

Whatever Oliver’s personal proclivities might be (we aren’t given any backstory), he and Elio both behave like everyone else, dancing and flirting with local girls at parties, reading books while lounging poolside in their swim trunks. They become friends, of a sort, though Elio is unsure how deep that friendship is, whether Oliver views him as a peer or as his professor’s kid. Through the summer, Elio simmers.

It all leads more or less where you’d expect it to, but director Luca Guadagnino (“I Am Love,” “A Bigger Splash”), working from André Aciman’s novel, lets it develop naturally, building on glances, implications, and indirect acknowledgments. The writer and producer is James Ivory, of the august Merchant-Ivory label, and his restraining influence can be felt. Elio and Oliver (and the other guests) are often wearing nothing but shorts, as is seasonally appropriate, so even incidental physical contact has an added charge, and their legs and torsos are lovingly photographed by cinematographer Sayombhu Mukdeeprom. But the film’s sexual activity is discreet, not exploitative, and the film leaves much unsaid. The word “gay” and its synonyms are never spoken except once in passing, referring to someone else. Any lengthy, angsty conversations Oliver and Elio may have about their secret love and the consequences of revealing it are held out of our hearing.

In that respect, “Call Me by Your Name” is different from many gay-relationship films, where the central conflict is that the relationship exists. Oliver and Elio’s liaison is certainly problematic — it’s a conflict — but the primary struggle is within Elio. To that end, Timothée Chalamet (who was 20 when the film was shot) gives an astonishingly sensitive performance, capturing the awkwardness and exuberance of unexpected love with devastating accuracy. Armie Hammer, who’s seldom been given an opportunity to shine, also does good work, adding a layer of tenderness to his foundation of natural charisma.

And then there’s Michael Stuhlbarg, coming through with a closing speech that encapsulates, with perfect clarity and insight, the themes of this beautiful, deeply erotic film. It’s an ode to love in all its forms, to the very idea of Love as an essential part of humanity that we should grab onto whenever it finds us. That the story happens to involve absurdly good-looking people is just icing on the peach.